How to join two 2D objects into one?
First apply transformations to your objects (Ctrl+A-->Loc, Rot&amp;Scale). Select your heart mesh, then the plane in Object Mode, then enter the Edit Mode of the plane, press Spacebar and type Knife Project. Extrude the plane a bit and give it a Remesh Modifier being in Object Mode. Apply the modifier, then delete extruded vertices. Finally join meshes with Ctrl+J. Correct some vertices position (merge them with Alt+M).